A method, electronic device and storage medium for identifying key stations in a subway network considering cascading failures

Abstract

The present invention discloses a method for identifying key stations in a subway network considering cascading failures, an electronic device, and a storage medium. Based on the constructed weighted time-varying subway network and the initial states and degree values of each station at each time period, the cascading failure process after station failures is simulated, and a passenger origin-destination-based passenger flow distribution rule is established to obtain the weighted time-varying subway network after cascading failures caused by failures of each station at each time period. Based on the node failure rate, network maximum connectivity rate, and network passenger flow intensity entropy after failures of each station at each time period, the comprehensive importance of each station at each time period is calculated, and the key subway stations at each time period are identified based on the comprehensive importance. The present invention is used to assist public transport operators in identifying key stations in the subway network at each time period, thereby providing decision support for the formulation of emergency plans under emergencies and providing a scientific basis for the emergency operation scheduling and management of the subway network.

Description

Technical Field

[0001] The invention relates to a method for identifying key sites in a subway network taking cascading failure into consideration, electronic equipment and a storage medium, and belongs to the technical field of public transportation planning and control. Background Art

[0002] With the acceleration of my country's urbanization process, the population density and travel demand of large and medium-sized cities have increased sharply. With the characteristics of high capacity, high timeliness and strong reliability, the subway has become the backbone network for medium and long-distance travel in the city. However, with the increase in the density of subway lines and the enhancement of the interaction between stations, higher requirements are also placed on the robustness of its network. The failure of local stations or operating sections may trigger cascading failures of the network through dynamic redistribution of passenger flow, resulting in a sharp drop in the transportation efficiency of the subway network or even paralysis, which will seriously affect the daily travel of residents. Especially during peak hours in the morning and evening or in emergency scenarios, the chain reaction of key station failures will aggravate the vulnerability of the network. Therefore, identifying key stations in the subway network that may cause large-scale cascading failures in different time periods can provide decision support for the formulation of emergency support plans under public emergencies, such as the operation plan of small routes of subway lines, the operation route and dispatching plan of shuttle vehicles, etc.

[0003] There are three main problems with existing key site identification methods:

[0004] First, most existing studies evaluate the importance of sites based on static network topology structures (such as degree centrality and betweenness centrality), ignoring the cascading failure phenomenon caused by the dynamic transfer of actual passenger flow between sites, and it is difficult to capture the cascading propagation path caused by site failure in real scenarios.

[0005] Second, most existing studies assume that the network is a static one, without considering the temporal heterogeneity of passenger flows in actual networks, and thus cannot reflect the time-varying characteristics of key stations in subway networks.

[0006] Third, most existing studies assume that when a key station fails, passenger flow will be transferred to surrounding stations with greater influence (influence is measured by degree, betweenness, flow intensity, etc.), without considering passengers' travel mode selection and travel path selection behavior, resulting in an inadequate description of the scale and propagation process of cascading failures.

[0007] Therefore, those skilled in the art urgently need to improve the identification of key sites in the subway network from the perspective of actual passenger flow. Summary of the invention

[0008] Objective: To overcome the deficiencies in existing key station identification methods for the subway network, which do not adequately consider the spatio-temporal heterogeneity of the actual passenger flow in the subway network and the cascading failure phenomenon caused by station failures in real scenarios, the present invention provides a method, an electronic device, and a storage medium for identifying key stations in a subway network considering cascading failures. Starting from the actual passenger flow perspective, a method for identifying key stations in a subway network that integrates the characteristics of "weighted-dynamic-cascading" is constructed, and the global impact of station failures is quantified from the perspective of the spatio-temporal evolution of passenger flow, which is used to assist public transportation operators in identifying key stations in the subway network at different times, thereby providing decision-making support for formulating emergency response plans in the event of emergencies and providing a scientific basis for the emergency operation scheduling and management of the subway network.

[0009] Technical solution: To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0010] In the first aspect, a method for identifying key stations in a subway network considering cascading failures includes the following steps:

[0011] Obtain subway line data and station data, and establish an unweighted subway network.

[0012] Based on the card-swipe data, obtain the OD pair travel volumes in the unweighted subway network at different times.

[0013] Taking the OD pair travel volumes at different times as inputs and the shortest passenger travel path length as the goal, based on the unweighted subway network, obtain the passenger flow volume of each edge in the network at different times, and establish a weighted time-varying subway network.

[0014] For the weighted time-varying subway network, calculate the degree value, flow intensity, and capacity limit of each station at different times.

[0015] Based on the flow intensity and capacity limit of each station at different times, calculate the initial state value of each station at different times.

[0016] Based on the constructed weighted time-varying subway network and the initial state and degree value of each station at different times, simulate the cascading failure process after station failures, and establish a passenger flow distribution rule considering the origin-destination of passengers, to obtain the weighted time-varying subway network after cascading failures caused by each failed station at different times.

[0017] Based on the weighted time-varying subway network after cascading failures, calculate the node failure rate of each failed station at different times.

[0018] Based on the weighted time-varying subway network after cascading failures, calculate the maximum network connectivity rate of each failed station at different times.

[0019] Based on the weighted time-varying subway network after cascading failures, calculate the network passenger flow intensity entropy of each failed station at different times.

[0020] Based on the node failure rate, network maximum connectivity rate and network passenger flow intensity entropy after the failure of each station in each time period, the comprehensive importance of each station in each time period is calculated, and the key subway stations in each time period are identified based on the comprehensive importance.

[0021] In a second aspect, a computer-readable storage medium is provided, characterized in that a computer program is stored thereon, and when the computer program is executed by a processor, a method for identifying key sites in a subway network taking into account cascading failures as described in any one of the first aspects is implemented.

[0022] According to a third aspect, a computer device includes:

[0023] Memory, used to store instructions.

[0024] The processor is used to execute the instructions so that the computer device performs the operations of the method for identifying key sites in a subway network considering cascading failures as described in any one of the first aspects.

[0025] Beneficial effect: The present invention provides a method for identifying key sites in a subway network taking cascading failure into consideration, an electronic device and a storage medium. By deeply mining subway passenger flow data, a subway weighted time-varying network is constructed. On this basis, an improved coupled map lattice (CML) model is used to characterize the cascading failure process caused by the failure of the site. The node failure rate, the maximum network connectivity rate and the network passenger flow intensity entropy are introduced to use the minimum entropy weight method to evaluate the network after the final cascading failure, and a method for identifying key sites in the network is constructed.

[0026] The key site identification method proposed in the present invention comprehensively considers the time-varying passenger flow characteristics and dynamic propagation characteristics of the site passenger flow. Compared with the traditional key site identification method based on static network topology structure, it can more accurately describe the cascading fault propagation process and dynamic evolution law of the network under actual emergency situations. In addition, compared with other cascading failure propagation models, the present invention considers the impact of the heterogeneity of passengers' travel origin and destination points on passenger flow distribution, and more accurately describes the passengers' travel mode selection behavior and travel path selection behavior. It can provide decision support for the determination of emergency plans for subway networks under public emergencies. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a flow chart of the key site identification method of the present invention.

[0028] Figure 2 Schematic diagram of a subway network in an embodiment of the present invention

[0029] Figure 3 It is a passenger flow distribution diagram within one day in an embodiment of the present invention.

[0030] Figure 4 It is a schematic diagram of the passenger flow distribution rule in the present invention, where: Figure 4 In (a), it is the schematic diagram of the station at s the moment of being affected by failure; Figure 4 In (b), it is the schematic diagram of the passenger flow distribution when the station is removed from the network at s +1 moment; Figure 4 In (c), it is the schematic diagram of the network topology structure after the station is removed from the network.

[0031] Figure 5 It is the distribution map of the top 50 stations with comprehensive importance from 8:00 to 9:00 in the embodiment of the present invention.

[0032] Figure 6 It is the distribution map of the top 50 stations with comprehensive importance from 12:00 to 13:00 in the embodiment of the present invention.

[0033] Figure 7 It is the distribution map of the top 50 stations with comprehensive importance from 17:00 to 18:00 in the embodiment of the present invention. Detailed implementation manners

[0034] Next, in combination with the accompanying drawings in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative efforts belong to the protection scope of the present invention.

[0035] Next, the present invention will be further described in combination with specific embodiments.

[0036] Embodiment 1:

[0037] This embodiment introduces a method for identifying key stations in the subway network considering cascading failures. As Figure 1 shown, it includes the following steps:

[0038] Step 1: Obtain the subway line data and station data within the research scope, and establish an unweighted subway network.

[0039] Step 2: Based on the historical card-swipe data, obtain the travel volume of each OD (ORIGIN-DESTINATION) pair in the unweighted subway network for each time period.

[0040] Step 3: Using the travel volume of each OD pair as the input and the shortest travel path length of passengers as the goal, based on the established unweighted subway network, obtain the passenger flow of each edge in the network for each time period, and establish a weighted time-varying subway network.

[0041] Step 4: For the subway weighted time-varying network, calculate the degree value, flow intensity, and capacity limit of each station in each time period.

[0042] Step 5: Based on the flow intensity and capacity limit of each station in each time period, calculate the initial state value of each station in each time period.

[0043] Step 6: Based on the constructed subway weighted time-varying network, the initial state, and degree value of each station in each time period, use the improved coupled map lattice (CML) model to simulate the cascading failure process after station failure, and establish a passenger flow distribution rule considering the origin-destination of passengers to obtain the subway weighted time-varying network after cascading failure of each failed station in each time period.

[0044] Step 7: Based on the subway weighted time-varying network after cascading failure, calculate the node failure rate of each failed station in each time period.

[0045] Step 8: Based on the subway weighted time-varying network after cascading failure, calculate the maximum network connectivity rate of each failed station in each time period.

[0046] Step 9: Based on the subway weighted time-varying network after cascading failure, calculate the network passenger flow intensity entropy of each failed station in each time period.

[0047] Step 10: Based on the node failure rate, maximum network connectivity rate, and network passenger flow intensity entropy of each failed station in each time period, use the entropy weight method to calculate the comprehensive importance of each station in each time period, and identify the key subway stations in each time period based on the comprehensive importance.

[0048] Further, the specific steps of Step 1 include:

[0049] Step 1.1: Based on the subway line and station data, establish an unweighted subway network using the method of constructing an entity network (e.g., Space L method) .

[0050] Among them, represents the unweighted subway network; represents the set of subway stations, N is the total number of stations in the subway network; represents the set of edges of the subway network. The adjacency matrix corresponding to the edge set E can be expressed as:

[0051] (1)

[0052] Among them, represents that station is directly connected to station , otherwise .

[0053] Further, step 2 specifically includes:

[0054] Step 2.1: Read the historical subway card - swiping data, which includes the passenger's card number, entry time, entry station, exit time, and exit station.

[0055] Step 2.2: According to the historical card - swiping data, count the travel volumes of OD pairs with the same origin and destination within each time period t and construct the travel volume matrix of passengers . Among them, is matrix, is the number of stations in the subway unweighted network. The elements in the travel volume matrix are denoted as , represents that the boarding time is within the time period t , the boarding station is station , and the alighting station is station 's travel volume.

[0056] Further, step 3 specifically includes:

[0057] Step 3.1: For the travel volume matrix of each time period, based on the constructed subway unweighted network G , use Dijkstra's algorithm to calculate the shortest path.

[0058] Step 3.2: Count the passenger flow of each shortest path passing through each edge in the subway network, denoted as , represents that the boarding time is within the time period t , and the passenger flow passing through the link of the subway network.

[0059] Step 3.3: According to the subway unweighted network G and the passenger flow on each link in each time period, establish the subway weighted time - varying network , where represents t the passenger flow of the subway network link in the time period, and its matrix can be expressed as:

[0060] (2)

[0061] Further, step 4 specifically includes:

[0062] Step 4.1: According to the established subway weighted time - varying network , calculate the degree value of the network stations, and its calculation formula is as follows:

[0063] (3)

[0064] Step 4.2: According to the established weighted time-varying subway network , calculate the traffic intensity of network stations , and its calculation formula is as follows:

[0065] (4)

[0066] (5)

[0067] (6)

[0068] Where: represents the traffic intensity passing through station t during the time period , and is the sum of the inbound passenger flow t and the outbound passenger flow during the time period .

[0069] Step 4.3: According to the established weighted time-varying subway network , calculate the capacity limit of each station in the subway network , and its calculation formula is as follows:

[0070] (7)

[0071] (8)

[0072] Where: is the maximum traffic intensity of station in all time periods ; is the last selected time period; and are the adjustment coefficients of the capacity limit, .

[0073] Furthermore, the said step 5 specifically includes:

[0074] Step 5.1: According to the traffic intensity and the capacity limit of each station in each time period, calculate the initial state value of each station in each time period, and its calculation formula is as follows:

[0075] (9)

[0076] Furthermore, the said step 6, as Figure 4 shown, specifically includes:

[0077] Step 6.1: Set the maximum number of iteration cyclesT , the initial state of all stations .

[0078] Step 6.2: Select any station as the failure object, and apply an external perturbation to the failed station at time step 1 R ( R ≥1), and make it fail. Then the state of the station at the next time can be expressed by formula (10). When the station fails at time step 1, the failed station is removed from the subway network at time step 1, and the state of the station is set to 0 for all subsequent times starting from time step 1.

[0079] (10)

[0080] Step 6.3: The stations directly connected to the station will be affected by the station at time step 1, and the subsequent station state values may exceed 1, thus triggering a new round of station failures. This process will continue to repeat until no more stations fail. Here, the improved coupled map lattice (CML) model in formula (11) is used to update the state values of all stations in the network at s +1 time step.

[0081] (11)

[0082] Wherein: represents the state value of the station t at time step +1 within the time period s , and can be used to determine whether the station can provide travel services at the current moment. If , then the station is in normal operation; if , then the station is in a congested or failed state; represents the topological connection relationship between stations; represents t the passenger flow weight flowing into the station at time step s +1 within the time period ; represents t the total passenger flow flowing into the station s at time step +1 within the time period is the topological coupling coefficient, is the passenger flow coupling coefficient, and ; s represents the time step, i.e., the number of iterations of the site status value under cascading failure propagation; is a non - linear mapping function used to describe the change of element status values in a chaotic dynamic system. Select as this non - linear mapping function to describe the dynamic behavior of stations in the subway network. When is true, .

[0083] Step 6.4: During the iteration of the CML model, after the failure of site is removed from the network, the passenger flow flowing into the failed site will re - select the next inflowing site according to the needs of the passenger flow itself. When the failed site is removed from the subway network at time step s +1, the passenger flow flowing from site to site will be assigned to other adjacent sites of site . The process of passenger flow weight allocation and update from site s +1 to site to site is shown in formulas (12) - (13) as follows:

[0084] (12)

[0085] St. (13)

[0086] Among them, represents other neighboring sites of site except ; represents the passenger flow weight from site s +1 to site to site ; represents the passenger flow weight from site s at time to site ; represents the passenger flow weight from site s at time to site ; is the passenger flow weight that can reach the destination through site s +1 after the failure of site . Its value calculation process is as follows: In the network after removing site where it can pass through site to reach the destination, the calculation process is as follows: In the network after removing site ​ Taking the current site as the starting point and the passenger flow destination in as the end point, use Dijkstra's algorithm to calculate the shortest path between two sites, and allocate the passenger flow at the sites on the shortest path to . Remove the passenger flow in where there is no shortest path from the network. The specific allocation process is as shown Figure 3 .

[0087] Step 6.5: According to s the passenger flow weight flowing from site to site at time +1 and the failed site , update the network , increment the time step s by 1, and repeat steps 6.3 - 6.4. If the time step , terminate the iteration and output the weighted time-varying subway network after cascading failure .

[0088] Furthermore, the node failure rate after the failure of each site in each time period in step 7 is calculated as follows:

[0089] (14)

[0090] where: represents t the node failure rate of the weighted time-varying subway network after cascading failure of the failed site in the time period; t represents the number of failed sites of the weighted time-varying subway network after cascading failure of the failed site

[0091] Furthermore, the maximum connectivity rate of the network after the failure of each site in each time period in step 8 is calculated as follows:

[0092] (15)

[0093] where: represents t the maximum connectivity rate of the weighted time-varying subway network after cascading failure of the failed site in the time period; represents the number of nodes in the largest connected subgraph of the weighted time-varying subway network after cascading failure of the failed site

[0094] Further, the entropy of the network passenger flow intensity after the failure of each station in each time period in step 9 is calculated as follows:

[0095] (16)

[0096] (17)

[0097] Where: represents the entropy of the weighted time-varying network passenger flow intensity of the subway after cascade failure of the failed station in the t-th time period

[0098] Further, step 10 specifically includes:

[0099] Step 10.1: Based on the node failure rate, the maximum network connectivity rate, and the entropy of the network passenger flow intensity after the failure of each station in each time period, establish a comprehensive evaluation matrix of the station , and the calculation formula is as follows:

[0100] (18)

[0101] Step 10.2: Normalize the comprehensive evaluation matrix to obtain the normalized comprehensive evaluation matrix , and the calculation formula is as follows:

[0102] (19)

[0103] Step 10.3: Calculate the information entropy of the three indicators of the node failure rate, the maximum network connectivity rate, and the entropy of the network passenger flow intensity 、 、 , and the calculation formula is as follows:

[0104] (20)

[0105] (21)

[0106] (22)

[0107] Step 10.4: Calculate the weights of the three indicators of the node failure rate, the maximum network connectivity rate, and the entropy of the network passenger flow intensity 、 、 , and the calculation formula is as follows:

[0108] (23)

[0109] (24)​

[0110] (25)

[0111] Step 10.5: Calculate the comprehensive importance of each station in each time period ; Sort the comprehensive importance of each station in descending order. The stations with higher rankings are the key stations in the subway network. Among them, the comprehensive importance is calculated as follows: The calculation formula is as follows:

[0112] (26)

[0113] Example 2:

[0114] This example introduces a computer-readable storage medium with a computer program stored thereon. When the computer program is executed by a processor, it implements a method for identifying key stations in a subway network considering cascading failures as described in any one of Example 1.

[0115] Example 3:

[0116] This example introduces a computer device, including:

[0117] A memory for storing instructions.

[0118] A processor for executing the instructions, causing the computer device to perform the operations of a method for identifying key stations in a subway network considering cascading failures as described in any one of Example 1.

[0119] Example 4:

[0120] This example introduces the process of applying a method for dynamically identifying key stations in a subway network considering cascading failures to identify key stations in the subway network of a certain city, as follows.

[0121] 1: Obtain subway line data and station data within the research scope, and establish an unweighted subway network.

[0122] Obtain subway line data and station data within the research scope. Among them, the subway station and line data include the following attributes: station number, station name, station longitude, station latitude, and line name. Specific data examples are shown in Table 1.

[0123] Table 1 Example of subway station and line data

[0124]

[0125] Based on the above data, use the Space L method to establish an unweighted and directed bus network and an unweighted and directed subway network . Among them,G Indicates the subway unweighted network; V Indicates the set of subway stations; E Indicates the set of edges of the subway network; During the construction of the subway network, stations with the same name but belonging to different lines are regarded as the same station. This network is an undirected network, containing 159 stations and 328 edges in total. The subway unweighted directed network is as Figure 2 shown.

[0126] 2: Based on the historical card-swipe data, obtain the travel volumes of OD pairs in each period of the subway unweighted network;

[0127] As Figure 3 shown, select the subway card-swipe data of three periods: the morning peak (8:00 - 9:00), the midday flat peak (12:00 - 13:00), and the evening peak (17:00 - 18:00) on April 12, 2019 as the research object. The subway card-swipe data includes OD numbers, entry times, entry stations, exit times, and exit stations, with a total of 381,120 pieces of data. Specific data examples are shown in Tables 2, 3, and 4.

[0128] Table 2 Example of subway card-swipe data in the morning peak

[0129]

[0130] Table 3 Example of subway card-swipe data in the midday flat peak

[0131]

[0132] Table 4 Example of subway card-swipe data in the evening peak

[0133]

[0134] According to the historical card-swipe data, count the travel volumes of OD pairs with the same origin and destination within a certain time period t . The statistical results are shown in Tables 5, 6, and 7. Based on Tables 5 - 7, establish the travel volume matrix of OD pairs within each period t . .

[0135] Table 5 Example of OD pair travel volume in the morning peak

[0136]

[0137] Table 6 Example of OD pair travel volume in the midday flat peak

[0138]

[0139] Table 7 Example of OD pair travel volume in the evening peak

[0140]

[0141] 3: Using the travel volume of each OD pair in each time period as the input and the shortest passenger travel path length as the objective, based on the established unweighted subway network, obtain the passenger flow volume of each edge in the network in each time period, and establish a weighted time-varying subway network;

[0142] For all OD pairs in each time period, on the constructed unweighted subway network G calculate the shortest path according to Dijkstra's algorithm, and the obtained shortest paths are shown in Tables 8, 9, and 10.

[0143] Table 8 Example of the shortest path of OD pairs during the morning peak

[0144]

[0145] Table 9 Example of the shortest path of OD pairs during the midday flat peak

[0146]

[0147] Table 10 Example of the shortest path of OD pairs during the evening peak

[0148]

[0149] Allocate the travel volume of OD pairs in each time period to each connecting edge on the obtained shortest path in an evenly distributed manner. Taking the OD pair numbered 1 during the morning peak as an example, the shortest path of this OD pair has only one section. Therefore, allocate all 98 passengers to the connecting edge from Zhonghuamen to Sanshanjie, and record the origin and destination of the allocated passenger flow.

[0150] According to the unweighted subway network G and the passenger flow allocated to the connecting edges of each station, establish a weighted time-varying subway network for each time period: morning peak , midday flat peak , evening peak .

[0151] 4: For the weighted time-varying subway network, calculate the degree value, flow intensity, and capacity upper limit of each station, where the adjustment coefficient of the capacity upper limit , . The degree value, flow intensity, and capacity upper limit of each station in each time period are shown in Tables 11, 12, and 13.

[0152] Table 11 Example of the degree value of each station

[0153]

[0154] Table 12 Example of the flow intensity of each station

[0155]

[0156] Example of Capacity Upper Limit of Each Station in Table 13

[0157]

[0158] 5: Calculate the initial state value of each station in each time period based on the traffic intensity and capacity upper limit of each station in each time period. The initial values of each station are shown in Table 14.

[0159] Table 14 Example of Initial State of Each Station

[0160]

[0161] 6: Based on the constructed subway weighted time-varying network and the initial state of each station, use the improved coupled map lattice (CML) model to simulate the cascading failure process after a station failure, and establish a passenger flow distribution rule based on considering the origin and destination of passengers.

[0162] Select the failure network as , select the failure station to apply the failure simulation of the cascading failure process after the station failure, and set the maximum iteration period T = 50, apply an external perturbation R = 4, topological coupling coefficient , passenger flow coupling coefficient . Use formula (10) to apply a perturbation to the failure station to make it fail.

[0163] s At time Figure 2 , the failure station is removed from the subway weighted time-varying network, and the edges connected to the failure station are removed. According to the passenger flow distribution rule, use formula (12) to re-distribute the passenger flow flowing into the failure station. The specific distribution process is as shown. Use formula (10) to update the states of other stations in the network, let s increment by 1, and repeat the above steps until

[0164] s , the process ends. becomes s fail, = 1, the Maigaoqiao station is removed from the network. The passenger flow flowing into the Maigaoqiao station from the adjacent Hongshan Zoo station (number: 2) leaves the subway network because it cannot reach the destination by detour, resulting in changing from 172 person-times at s = 0 to 0 person-times at s = 1 and will not increase subsequently.

[0165] The interference received by the Maigaoqiao station radiates from the center to the surrounding areas, affecting the surrounding stations, resulting in the state of the Hongshan Zoo station changing from Becomes Invalid, and peripheral stations are also interfered to varying degrees, thus triggering a new round of station failures. This process will continue continuously with the change of s until no more stations fail and the network resumes stability. When this occurs, the iterative process ends.

[0166] 7: For the subway weighted time-varying network, calculate the node failure rate after each station fails at each time period.

[0167] According to the network state after the evolution of the CML model ends, calculate the node failure rate after different stations fail at each time period through formula (14) , and the results are shown in Table 15.

[0168] Table 15 Node failure rates after different stations fail at each time period Example

[0169]

[0170] 8: For the subway weighted time-varying network, calculate the maximum network connectivity rate after each station fails at each time period;

[0171] According to the network state after the evolution of the CML model ends, calculate the maximum network connectivity rate after different stations fail at each time period through formula (15) , and the results are shown in Table 16.

[0172] Table 16 Maximum network connectivity rates after different stations fail at each time period Example

[0173]

[0174] 9: For the subway weighted time-varying network, calculate the entropy of network passenger flow intensity after each station fails at each time period;

[0175] According to the network state after the evolution of the CML model ends, calculate the entropy of network passenger flow intensity after different stations fail at each time period through formula (16) , and the results are shown in Table 17.

[0176] Table 17 Entropies of network passenger flow intensity after different stations fail at each time period Example

[0177]

[0178] Step 10: Based on the node failure rate, maximum network connectivity rate, and entropy of network passenger flow intensity of each station at each time period, use the entropy weight method to calculate the comprehensive importance of each station at each time period, and identify the key subway stations at each time period based on the comprehensive importance.

[0179] Based on the node failure rate, network maximum connectivity rate, and network passenger flow intensity entropy of stations in each time period, first establish a comprehensive evaluation matrix as shown in Equation (18). Then, normalize this matrix to obtain the normalized comprehensive evaluation matrix. Next, use Equations (20)-(22) to calculate the information entropy of the node failure rate, network maximum connectivity rate, and network passenger flow intensity entropy in each time period, and the calculation results are shown in Table 18. On this basis, use Equations (23)-(25) to calculate the weights of the node failure rate, network maximum connectivity rate, and network passenger flow intensity entropy in each time period, and the calculation results are shown in Table 19. Finally, calculate the comprehensive importance of each station in each time period based on Equation (26), and the example results are shown in Table 20. Sort the comprehensive importance of each station in descending order. The higher the ranking of a station, the larger the scale of cascading failures it causes to the subway network and the more affected passenger flow. Figure 5 、 Figure 6 、 Figure 7 Figure 50 shows the distribution map of the top 50 stations with comprehensive importance in each time period based on the calculation results in Table 20.

[0180] Table 18 Information Entropy of Node Failure Rate, Network Maximum Connectivity Rate, and Network Passenger Flow Intensity Entropy in Each Time Period

[0181]

[0182] Table 19 Weights of Node Failure Rate, Network Maximum Connectivity Rate, and Network Passenger Flow Intensity Entropy in Each Time Period

[0183]

[0184] Table 20 Comprehensive Importance of Stations in Each Time Period of the Subway Network

[0185]

[0186] The present invention discloses a method for dynamically identifying key stations in a subway network considering cascading failures. Based on subway card-swipe data, the OD pair travel volumes at different times in the subway network are obtained. Taking the OD travel volumes at each time period as inputs and the shortest passenger travel path length as the optimization objective, the passenger flow volume on each edge in the subway network at each time period is obtained, and a weighted time-varying subway network model is constructed. For the weighted time-varying subway network, the flow intensity and capacity limit of each station at each time period are calculated, so as to quantify the initial state of each station at each time period. An improved coupled map lattice (CML) model is introduced to simulate the cascading propagation process after station failures, and a dynamic reassignment rule based on passenger origin-destination is embedded to characterize the coupling effect of fault propagation and passenger flow time-varying characteristics. Through multi-dimensional indicators such as node failure rate, network maximum connectivity rate, and passenger flow intensity entropy, combined with the entropy weight method, the comprehensive importance of each station at each time period is calculated, and finally the dynamic identification of key stations is realized. The present invention can help subway operation enterprises quickly identify key stations that may trigger large-scale cascading failures at each time period, and provide decision-making support for the formulation of emergency plans under emergencies.

[0187] The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for identifying critical stations in a subway network considering cascading failures, characterized in that: It includes the following steps: Obtain subway line data and station data, and establish an unweighted subway network; Based on the card-swipe data, obtain the OD pair travel volumes in the unweighted subway network for each time period; Taking the OD pair travel volumes for each time period as the input and the shortest passenger travel path length as the goal, based on the unweighted subway network, obtain the passenger flow volume of each edge in the network for each time period, and establish a weighted time-varying subway network; For the weighted time-varying subway network, calculate the degree value, flow intensity, and capacity upper limit of each station for each time period; Based on the flow intensity and capacity upper limit of each station for each time period, calculate the initial state value of each station for each time period; Based on the constructed weighted time-varying subway network and the initial state and degree value of each station for each time period, simulate the cascading failure process after the station fails, and establish a passenger flow distribution rule considering the origin and destination of passengers to obtain the weighted time-varying subway network after cascading failure of each failed station for each time period; Based on the weighted time-varying subway network after cascading failure, calculate the node failure rate of each failed station for each time period; Based on the weighted time-varying subway network after cascading failure, calculate the maximum network connectivity rate of each failed station for each time period; Based on the weighted time-varying subway network after cascading failure, calculate the network passenger flow intensity entropy of each failed station for each time period; Based on the node failure rate, maximum network connectivity rate, and network passenger flow intensity entropy of each failed station for each time period, calculate the comprehensive importance of each station for each time period, and identify the key subway stations for each time period based on the comprehensive importance; The obtaining of the weighted time-varying subway network after cascading failure of each failed station for each time period specifically includes: Step 6.1: Set the maximum number of iterations T and the initial states of all stations Step 6.2: Select any station v i as the failure object, apply an external perturbation R to the failed station at time step 1 to make it fail; calculate the state of station v i at the next When station v fails at time step 1 i after failure, the failed station v i is removed from the subway network at time step 1, and the state of the station is set to 0 for all subsequent times starting from time step 1; Step 6.3: The sites directly connected to site v i will be affected by site v at time step 1, triggering a new round of site failures. The site failure process will repeat continuously until no more sites fail, and the state values of all sites at time step s + 1 are obtained i The expression is as follows: The expression is as follows: Wherein: represents the state value of site v at time step s + 1 within time period t. If i then site v is in a normal operating state; if i then site v is in a congested or failed state; a i represents the topological connection relationship between sites; ji represents the passenger flow weight flowing into site v at time step s + 1 within time period t for site v j i ; represents the total passenger flow flowing into site v at time step s + 1 within time period t for site v i ; ε1 is the topological coupling coefficient, ε2 is the passenger flow coupling coefficient; s represents the time step; f(x) is a non - linear mapping function, i, j ∈ [1, N], where N is the total number of sites in the subway network; K i represents the degree value of site v i ; represents the state value of site v at time step s + 1 within time period t j ; represents the state value of site v at time step s within time period t i ; Step 6.4: During the iterative process of the state values of all stations at time step s + 1, when the failed station v i is removed from the subway network at time step s + 1, the passenger flow j flowing into station v i will be assigned to other adjacent stations of station v , and the passenger flow weight j from station v j to station v w at time s + 1 is obtained. The expression is as follows: The expression is as follows: where w represents the neighboring stations of station v other than v j except v i ; represents the passenger flow weight from station v to station v at time s + 1 j ; w ; represents the passenger flow weight from station v to station v at time s j ; w ; represents the passenger flow weight from station v to station v at time s j ; i ; is the passenger flow weight that can reach the destination via detouring through station v after station v fails at time s + 1 i ; ; w ; Among them, The acquisition method is as follows: In the network G i after removing the site v t starting from the current site v j as the starting point and with the passenger flow destination in j as the end point, calculate the shortest path between the two sites, and allocate the passenger flow in w where the next site of the site v on the shortest path and where there is a shortest path to Step 6.5: According to the passenger flow weight flowing from station \(v\) at time \(s + 1\) j to station \(v\) w and the failed station \(v\) update the network \(G\) i . Increment the time step \(s\) by 1, and repeat Steps 6.3 - 6.

4. If the time step \(s>T\), terminate the iteration and output the weighted time-varying subway network \(G\) after cascading failures t . t .

2. The method for identifying key stations in a subway network considering cascading failures according to claim 1, wherein: The obtaining of the OD pair travel volumes in the unweighted subway network for each time period specifically includes: Read the subway card-swipe data, which includes the passenger's card number, entry time, entry station, exit time, and exit station; According to the card - swiping data, count the travel volume of OD pairs with the same origin and destination within each time period t, and construct the travel volume matrix OD of passengers. t ; Among them, OD t is an N×N matrix, where N is the number of stations in the unweighted subway network; the elements in the travel volume matrix OD t are denoted as indicating the travel volume when the boarding time is within the time period t, the boarding station is station v i , and the alighting station is station v j .

3. A method for identifying key stations in a subway network considering cascading failures according to claim 1, characterized in that: The establishment of the weighted time-varying subway network specifically includes: OD trip volume matrix for each time period t , based on the constructed subway unweighted network G, use Dijkstra's algorithm to calculate the shortest path; Count the passenger flow through each edge in the subway network for the shortest path in each time period, denoted as w ij t , w ij t represents the passenger flow through the link e in the subway network when the boarding time is within the time period t ij ; According to the subway unweighted network G and the passenger flow of each link in each time period, a subway weighted time-varying network G is established. t =(V,E,W t ), V = {v i |i∈[1,N]} represents the set of subway stations, N is the total number of stations in the subway network; E={e ij |i,j∈[1,N],i≠j} represents the edge set of the subway network, where W t ={w ij t |i,j∈[1,N],i≠j} represents the passenger flow of the subway network edge during period t as follows:

4. A method for identifying key stations in a subway network considering cascading failures according to claim 1, characterized in that: The calculation of the degree value, flow intensity, and capacity upper limit of each station for each time period specifically includes: According to the established subway weighted time-varying network G t , calculate the degree value K of the network sites i The expression is as follows: where a ij is an element of the adjacency matrix corresponding to the edge set E, i, j ∈ [1, N], and N is the total number of stations in the subway network; According to the established subway weighted time-varying network G t , calculate the traffic intensity S i (t) The expression is as follows: Wherein: is the passenger flow through the edge e of the subway network when the boarding time is within the time period t ij , S i (t) represents the flow intensity through the station v i during the time period t, is the inbound passenger flow during the time period t, is the outbound passenger flow during the time period t; Based on the established weighted time-varying subway network G t , calculate the capacity upper limit C of each station in the subway network i The expression is as follows: Wherein: is site v i is the maximum flow intensity during all time periods {t1, t2, t3,..., t M}, t M is the last selected time period, and α and β are adjustment coefficients for the capacity upper limit.

5. The method for identifying key stations in a subway network considering cascading failures according to claim 1, characterized in that: The calculation of the initial state value of each station for each time period specifically includes: According to the traffic intensity S i (t) and the capacity limit C i of each site in each time period, calculate the initial state value of each site in each time period The expression is as follows:

6. A method for identifying key stations in a subway network considering cascading failures according to claim 1, characterized in that: The expression of the node failure rate after the failure of each station for each time period is as follows: Where: I i (t) represents the failure rate of the nodes in the weighted time-varying subway network after cascading failures of the failure site v i at time period t; Fn i (t) represents the failure rate of the failure site v i in the weighted time-varying subway network G t after cascading failures, and the number of failed sites; N is the total number of sites in the subway network The expression of the maximum network connectivity rate after the failure of each station for each time period is as follows: Where: LC i (t) represents the failed site v at time period t i The maximum connectivity rate of the weighted time-varying subway network after cascading failure; represents the failed site v at time period t i The weighted time-varying subway network G after cascading failure t The number of nodes in the largest connected subgraph of; The network passenger flow intensity entropy after the failure of each station for each time period, the calculation formula is as follows: Among them: E i (t) represents the number of failed stations v in the t-th time period i The entropy of the weighted time-varying network passenger flow intensity of the subway after the final cascading failure, S i (t) represents the flow intensity passing through station v within the t-th time period i of.

7. A method for identifying key stations in a subway network considering cascading failures according to claim 1, characterized in that: The identifying of the key subway stations for each time period based on the comprehensive importance specifically includes: Based on the node failure rate, the maximum network connectivity rate, and the network passenger flow intensity entropy after failure at each station in each time period, a comprehensive evaluation matrix X of the station is established t ; For the comprehensive evaluation matrix X t perform normalization processing to obtain the normalized comprehensive evaluation matrix Calculate the information entropy of three indicators: node failure rate, network maximum connectivity rate, and network passenger flow intensity entropy Calculate the weights of three indicators: the failure rate of computing nodes, the maximum network connectivity rate, and the entropy of network passenger flow intensity The expressions are as follows: Calculate the comprehensive importance of v at each site for each period i Sort the comprehensive importance of each site in descending order. The site with a higher ranking is a key site in the subway network. Among them, the comprehensive importance The expression is as follows:​ 8. A computer-readable storage medium, characterized in that: It stores a computer program, which when executed by a processor, implements a method for identifying key subway stations in a subway network considering cascading failure as described in any one of claims 1 to 7.

9. A computer device, characterized in that: It includes: A memory for storing instructions; A processor for executing the instructions, so that the computer device performs the operations of a method for identifying key subway stations in a subway network considering cascading failure as described in any one of claims 1 to 7.

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